If your point here is that your hypothetical was ridiculous and completely impossible and therefore had zero relevance to the real world, then I'll agree.
Either you would call in the bulldozers or you wouldn't.
I would call in the bulldozers. But not in your hypothetical (which CANNOT EXIST).
Again (since it didn't seem to sink in the first time), you cannot know with absolute certainty that such-and-such group of critters is the last group of their species on earth. You simply can't.
A more realistic scenario is this: The government - or rather, ideologues who work for one department of the government - informs you that your pond contains the last surviving colony of such-and-such critter (according to their records, or their database, or the latest memo they received, or the latest "List" of "Endangered" species drafted up by some lawyers they pay...)
That would be a more realistic and informative hypothetical scenario for discussion. Question number one would be: Do you believe the government on such matters? Is the government always right?
Does the government, especially enviro-ideologues in its pay, have a great track record in stewardship of the environment?
I know the answers to these questions, and I think you do too. But if you prefer to gaze dreamily upon your Completely-Impossible Hypothetical, go right ahead....
No I don't. If I had the answers, I wouldn't have asked the question. Glad to see your world is black and white though.